Heat Pipes for a Single Well Engineered Geothermal System

ABSTRACT

A heat pipe or a bundle of heat pipes for transporting geothermal heat in a well is provided. As the temperature rises at one end of the heat pipe, the operating fluid turns to a vapor which absorbs the latent heat. The hot vapor within the heat pipe flows to the cooler end of the heat pipe where it then condenses and releases the latent heat. The condensed fluid then flows back to the hot side of the heat pipe and the process repeats itself.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/061,444 filed Oct. 8, 2014, which is herebyincorporated by reference in its entirety.

BACKGROUND OF THE INVENTION

Heat pipes are used to transport heat in a geothermal well to thesurface. A heat pipe needs to survive in caustic environments. TheSalton Sea is the worst environment discovered. The pH of theenvironment can be 5.5 and typical chemical composition concentration ofproduced fluids in parts per million (ppm) includes:

TABLE 1 Concentration Hydrogen (H⁺) ND Lithium (Li⁺) 187 Beryllium(Be⁺²) ND Ammonium (NH₄ ⁺) 369 Sodium (Na⁺) 50,169 Magnesium (Mg⁺²) 39Aluminum (Al⁺³) ND Potassium (K⁺) 12,784 Calcium (Ca⁺²) 24,584 Chromium(Cr⁺³) ND Manganese (Mn⁺²) 983 Iron (Fe⁺²) 1,180 Nickel (Ni⁺²) ND Copper(Cu⁺²) 4 Zinc (Zn⁺²) 320 Rubidium (Rb⁺) 69 Strontium (Sr⁺²) 443 Silver(Ag⁺) ND Cadmium (Cd⁺²) 1 Antimony (Sb⁺³) 1 Cesium (Cs⁺) 12 Barium(Ba⁺²) 177 Mercury (Hg⁺²) ND Lead (Pb⁺²) 79 Bicarbonate (HCO₃ ⁻) 69Nitrate (NO₃ ⁻) ND Fluorine (F⁻) 20 Sulfur Monoxide (SO⁻²) 98 Chlorine(Cl—) 137,670 Arsenate (AsO₄−3) 20 Selenate (SeO₄ ⁻²) ND Bromine (Br⁻)89 Iodine (I⁻) 10 Silicon Dioxide (SiO₂) 433 Carbon Dioxide (CO₂) 3,309Boric Acid (B[OH]₃) 1,800 Hydrogen Sulfide (H₂S) 15 Ammonia (NH₃) 59Methane (CH₄) 10 Total Dissolved Solids 235,000

What is needed is a heat pipe that can withstand such harsh environmentsfor an extended period of time without requiring replacement, and whichcan effectively transport heat in a geothermal well.

SUMMARY OF THE INVENTION

The present invention relates to heat pipes and heat pipe bundles. Inaccordance with the invention, heat pipes contain fluids that operate ina vacuum. Each heat pipe is self-contained. Many heat pipes are placedin a single well engineered geothermal system HeatNest™ system in orderto increase the efficiency of the process of capturing the far rockheat. In a ColdNest™ system, the heat pipes transfer the heat to the airand ground. Examples of applicant's HeatNest™ and ColdNest™ systems canbe found described in applicant's U.S. patent application Ser. Nos.14/114,939 filed Jan. 28, 2015 (U.S. Patent Application Publication No.US2015/0163965) and 14/114,946 filed Jan. 28, 2015 (Publication No.US2015/0159918), which are hereby incorporated by reference in theirentireties. As the temperature rises at one end of the heat pipe, theoperating fluid turns to a vapor which absorbs the latent heat. The hotvapor within the heat pipe flows to the cooler end of the heat pipewhere it then condenses and releases the latent heat. The condensedfluid then flows back to the hot side of the heat pipe and the processrepeats itself. The heat pipes are slanted at a minimum angle of threedegrees to facilitate the condensate returning to the bottom of the heatpipe. This transfer of heat takes place in only a few seconds.Conversely, when the heat source is removed, the heat pipes cool in onlya few seconds.

According to embodiments of the invention, a heat pipe bundle can beprovided composed of individual heat pipes that may carry seventeen kWof thermal power over a 120 feet length when operating at 190° C. at thecold end of the pipe, and have an outside diameter of 1¾ inches.

The heat pipe bundle will have a tip in the form of a nose conespecifically designed to facilitate insertion into the drilledappendage. The appendage hole diameter is to be at least ¾ inches largerthan the diameter of the heat pipe bundle. The heat pipe bundle can beinserted into a curved appendage hole with a twenty-five foot bendradius without compromising structural integrity due to bending stressesand abrasion against granitic hardness and rough rock.

The heat pipe bundle will have a central “carrier tube”, “mud tube” orchamber with an internal diameter of at least one inch that will allowfluid circulation through the heat pipe bundle interior and attachmentof an insertion and release device at the back end of the bundle duringinstallation.

The heat pipes can withstand external fluid pressures of 450 bars. Theheat pipes use materials and a design approach targeting a forty yearlife expectancy when exposed to corrosive fluids and temperaturescorresponding to the Salton Sea, described above. If the brine contentat a different site varies significantly from this specification, thaneither the life expectancy of the existing heat pipe design will bemodified.

The heat pipes and heat pipe bundles may not have an external coveringlayer on the external metal surface, which can significantly retard heattransfer into or out of the external metal surfaces of the heat pipebundle, with specific concern focused on open fluid exposure to maximizeconvective heat transfer mechanisms.

According to an aspect of the invention, an apparatus is provided fortransporting geothermal heat from a geothermal well to a surface. Theapparatus comprises at least one heat pipe comprising a wall surroundinga central tube or chamber, a fluid contained within the central tube orchamber, a first apparatus end that is closed and positioned at a firstend of the heat pipe, and a second apparatus end that is closed andpositioned at a second end of the heat pipe. The apparatus is configuredto be in a vertical or inclined position in the geothermal well, andfurther, the fluid absorbs geothermal heat at the first apparatus end asit transitions to a vapor, rises to the second apparatus end, releasesgeothermal heat at the second apparatus end as it condenses back to aliquid state, and returns to the first apparatus end. The firstapparatus end is configured for placement in the geothermal well and thesecond apparatus end is configured for placement near the surface. Thefluid in the chamber can be water.

According to one embodiment of the apparatus, the wall of the at leastone heat pipe includes a copper layer surrounding the central tube orchamber, a steel layer surrounding the copper layer; and a titaniumlayer surrounding the steel layer. At least the copper layer and thetitanium layer are non-porous to water.

According to a further embodiment of the apparatus, the wall of the atleast one heat pipe includes an internal coating layer surrounding thecentral tube or chamber, an iron layer surrounding the internal coatinglayer, which is configured to protect the iron layer from the fluid inthe central tube or chamber, and an external coating layer of a causticresistant material surrounding the iron layer. At least the internal andexternal coating layers are non-porous to water.

According to further embodiments of the invention, the at least one heatpipe can be made from titanium, copper or a copper-nickel alloy.

In accordance with one embodiment of the invention, the at least oneheat pipe includes a plurality of pipes welded together vertically, abase section secured to a base of the plurality of pipes, a threadedplug configured to be secured to an uppermost pipe of the plurality ofpipes, which comprises corresponding threading, and a port comprised inthe uppermost pipe of the plurality of pipes and positioned so as to becovered by the threaded plug when the threaded plug is fully insertedinto the uppermost pipe. During assembly of the at least one heat pipe,the threaded plug is partially inserted into the plurality of pipes, thefluid is injected into the at least one heat pipe through the port, andthe threaded plug is then inserted further into the plurality of pipesto cover the port. In this embodiment, the plurality of pipes, thethreaded plug and the base section can be made from titanium or anothermaterial.

According to a further embodiment of the apparatus of the presentinvention, the at least one heat pipe comprises a plurality of heatpipes arranged in a bundle surrounding a bundle central tube or chambercomprising the fluid. The bundle of heat pipes comprises at least sixheat pipes surrounding the bundle central tube or chamber, each of theheat pipes comprising a wall surrounding a central tube or chamber. Inan additional embodiment, the bundle of heat pipes comprises a pluralityof bundles of heat pipes. The plurality of bundles of heat pipescomprises at least six bundles of heat pipes and comprises a total of atleast seventy-two heat pipes. The plurality of bundles of heat pipes arearranged to surround a further central tube or chamber comprising thefluid.

The at least one heat pipe in accordance with the apparatus of the firstaspect of the invention may also comprise appendages branching outwardlyfrom a central heat pipe configured to insertion into horizontal orangled bore holes in the geothermal well.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 shows a heat pipe according to an embodiment of the invention.

FIG. 2 shows a heat delivery system according to an embodiment of theinvention.

FIG. 3 shows a cross-section of a first embodiment of a heat pipeaccording to the present invention.

FIG. 4 shows a cross-section of a second embodiment of a heat pipeaccording to the present invention.

FIG. 5 shows a cross-section of a third embodiment of a heat pipeaccording to the present invention.

FIG. 6 shows an embodiment of converting a titanium pipe into a heatpipe according to the third embodiment of the present invention.

FIG. 7a shows a first heat pipe design option according to the presentinvention.

FIG. 7b shows a second heat pipe design option according to the presentinvention.

FIG. 7c shows a third heat pipe bundle design option according to thepresent invention.

FIG. 8 shows a graph of estimated well electric power output for ageothermal field.

FIG. 9 shows an embodiment of a heat nest according to the inventionhaving appendages.

FIGS. 10a-10b show embodiments of a heat pipe according to the inventionhaving appendages.

FIGS. 11a-11d show an example of typical brine flow in a well.

FIG. 12 shows an example of creating appendages in a well.

FIG. 13 shows an example of an entrainment model.

FIGS. 14a-14c show examples of heat pipe bundle designs according to theinvention in two dimensions.

FIGS. 15a-15c show examples of heat pipe bundle designs according to theinvention in three dimensions.

DETAILED DESCRIPTION OF THE FIGURES

The present invention will now be described with reference made to FIGS.1-15 c.

A heat pipe 10 is shown in FIG. 1 having a first end 11 and a second end12. The heat pipe 10 is self-contained and includes fluids operating ina vacuum. As the temperature rises at one end 11 of the heat pipe 10,the operating fluid turns to a vapor which absorbs the latent heat. Thehot vapor within the heat pipe 10 flows to the cooler end 12 of the heatpipe where it then condenses and releases the latent heat. The condensedfluid then flows back to the hot end 11 of the heat pipe 10. The processof the liquid vaporizing and condensing at the two ends 11 and 12 of theheat pipe 10 repeats itself. In a preferred embodiment, the heat pipe 10is slanted at a minimum angle of three degrees to facilitate thecondensate returning to the bottom end 11 of the heat pipe 10. Thistransfer of heat takes place in only a few seconds. Conversely, when theheat source is removed, the heat pipes cool in only a few seconds.

Many heat pipes 10 can be used in a geothermal well 201. One or moregeothermal well 201, as shown in FIG. 2, are drilled into the earthuntil the required temperature is encountered in an area referred to asa heat reservoir 210. For example, the well 201 may have a diameter of17.5 inches (0.45 meters) drilled into a region of hot rock. The well201 may include lateral bore holes 207 drilled into the rock which areinstalled with heat pipes 208 to harvest heat and deliver it to thecentral well. A heat exchanger 209 transfers the heat from the heatpipes 208 to the closed cycle system 204. The heat is then pumped to thesurface using a pump 202, and delivered to the production well.Insulation 203, 206 and a high heat conductive material 205 are providedin the well to minimize heat loss. The heat delivered is based on theheat resource encountered in the earth. If enough heat is encounteredthe operational cost of the heat source is minimized because no fossilfuel is burned to generate the required amount of heat to change the oilviscosity. The geothermal well 201 can be depreciated over a long periodof time and thus the operational costs are composed of running thepumps. Geothermal well 201 can be used alone or in combination with aboiler 212 and waste heat 213 to provide the required thermal energy.

A boiler 212 can be used to augment the geothermal well 201 or replacethe geothermal well 201 for the heat required. The boiler 212 can alsoburn fossil fuel, crude oil or gas that naturally comes from an oilwell, such as flaring gas.

Additionally, if an additional heat source 213, such as waste heat orelectrical resistant heat, is available, the other heat source 213 canbe used to supply additional heat. For example, on an offshore oilplatform where it would be more difficult to implement a geothermalwell, waste heat or a combination of waste heat, electrical heat and/ora boiler can be used to supply the heat source for heating and/orflooding the oil reservoir. The other heat source 213 supplies heat to amanifold 218, such as a hot water manifold, for providing the hot waterto applications requiring the thermal output.

In accordance with the invention, multiple constructions of the heatpipe can be provided According to a first embodiment shown in FIG. 3, aheat pipe 30 is provided that includes a central chamber 31 surroundedby a layer of copper 32. The internal copper layer 32 may have athickness of 1.25 millimeters, but can vary in other embodiments. Asteel layer 33 is provided around the copper layer 32 and an outer layer34 of titanium is provided. The outer layer 34 of titanium may have athickness of one millimeter, but can vary in other embodiments. The heatpipe 30 has an inner diameter D₁ of twenty-eight millimeters and anouter diameter D₂ of 44.5 millimeters. The titanium 34 and copper 32 inthe heat pipe 30 are non-porous to water. In a preferred embodiment, theheat pipe 30 has a length of forty feet and can tolerate a temperatureinside the central chamber 31 of approximately 600° F.

According to a second embodiment, shown in FIG. 4, a heat pipe 40 isprovided that includes a central chamber 41 surrounded by iron 43. Theiron 43 piping has a layer of an internal coating 42 that protects theiron 43 from water flowing through the central chamber 41 of the heatpipe 40. The internal coating layer 42 may have a thickness of 1.25millimeters, but can vary in other embodiments. Another layer of causticresistant coating 44 is provided around the exterior of the iron layer42. The outer layer of coating 44 may have a thickness of onemillimeter, but can vary in other embodiments. The coating layer 44protects the iron 43 from exposure to caustic materials. The heat pipe40 may have an inner diameter D₃ of twenty-eight millimeters and anouter diameter D₄ of 44.5 millimeters. The exterior coating 44 andinterior coating 42 of the heat pipe 40 are non-porous to water. In apreferred embodiment, the heat pipe 40 has a length of forty feet andcan tolerate a temperature inside the central chamber 41 ofapproximately 600° F.

A third embodiment of a heat pipe 50 is shown in FIG. 5. The heat pipe50 includes a central chamber 51 surrounding by a titanium pipe 52. Thetitanium pipe 52 can have a thickness of 3.63 millimeters. In certainembodiments, the thickness of the titanium pipe 52 can vary depending onthe depth of the well and other factors. The inner diameter D₅ of theheat pipe 50 can be forty-one millimeters and the outer diameter D₆ canbe 48.26 millimeters (1.9 inches).

An embodiment for converting titanium pipes into a heat pipe 60 is shownin FIG. 6. Several titanium pipes 61 are attached by welds 62. A base 63is provided and welded to the titanium pipes 61. The topmost pipe 61 ishighly threaded, and a threaded plug 64 is screwed into the threadedpipe 61. A port 65 is provided near the top of the titanium pipes 61.When the threaded plug 64 is screwed into the threaded pipe 61, the port65 is left uncovered by the plug 64. Water is injected into the heatpipe 60 through the port 65. After the appropriate amount of water ispumped into the heat pipe 60, the port 65 is used to create a vacuum.The threaded plug 64 is then further screwed into titanium pipes 61 inorder to cover the port 65, thereby securing the vacuum. The threadedplug 64 can then be welded to the titanium pipes 61.

FIG. 7a shows a design for a heat pipe 70 a having an outer diameter of3.25 inches and four inch appendages. The heat pipe 70 a includes acentral chamber surrounded by a wall 72 a. The thermal capacity of thedesign is approximately 60 kW and may cost approximately $0.20/W.

FIG. 7b shows a design for a heat pipe 70 b having an outer diameter of5.25 inches and six inch appendages. The heat pipe 70 b includes acentral chamber 71 b surrounded by a wall 72 b. The thermal capacity ofthe design is approximately 120 kW and may cost approximately $0.22/W.

In contrast to the single tube designs of FIGS. 7a and 7b , FIG. 7cshows a heat pipe 70 c having a six-tube bundle design. Six individualpipes 72 c are bundled together around a central chamber 71 c. Each ofthe individual heat pipes 72 c includes a tube or chamber 73 c.

The thermal capacity of the design is approximately 100 kW and may costapproximately $0.18/W.

FIG. 8 shows the estimated well electric power output for a geothermalfield. The chart shown is based on a performance estimate based on WellPGM-11 Characteristics for a 1500 meter well depth and a 0.3 meter welldiameter. The elliptical region 80 represents the performance estimaterange. The brine natural convection defines the production limit in the10 to 1000 mD (millidarcy) mid-porosity region. The maximum values areset by a two millimeter per second brine flow rate, which is approachingpure fluid natural convection flow velocities. There is no performancedecay over time projected. In certain embodiments of the invention, theheat pipe in a heat nest is provided with a plurality of appendages. Asshown in FIGS. 9-10 b, a heat pipe 90 can have several appendages 91that branch outwardly from the heat pipe 90. The appendages 91 may havea single pipe design, such as the design of FIG. 7a or 7 b, or can havea bundle of pipes, such as the design of FIG. 7 c.

FIGS. 11a-11d show typical brine flow in a well. Large scale brinecirculation enables long term heat harvesting from the hottest zones.Heat pipes lower in the well benefit from higher fluid speed, but sufferfrom lower brine temperatures. The net effect is that all heat pipestransport about the same amount of heat. Large scale brine flowcirculation also enables heat harvesting from a large reservoir volumewith little impact on far field temperatures, as shown in FIGS. 11c -11d.

FIG. 12 shows an exemplary embodiment for drilling a bore hole 120 intoa formation 125 for receiving an appendage of a heat pipe and providingthe appendage. The bore hole 120 can be drilled laterally either beforeor after casing the well, if a well casing 123 is used. The drillingwhip stock 121 is anchored at a vertical location. Individual appendagebore holes 120 are drilled. The drilling apparatus is rotated andcleared from the bore hole 120. A heat pipe and grout feed tube are feddown the central bore hole 122 of the well by way of coiled tubing. Thewhip stock 121 guides the heat pipe into the appendage 120. Grout 124 ispumped into the appendage 120 to fill voids in non-aqueous or highlycorrosive environments. The whip stock 121 can be raised to the nextheight and rotated 90 degrees for use in creating another bore hole andproviding an appendage. It is estimated that using this method, fourappendages can be produced per day. Additional examples of creating anappendage can be found in applicant's co-pending U.S. patent applicationSer. No. 14/202,778 titled “Creation of SWEGS Appendages and Heat PipeStructures”, filed Mar. 3, 2014, (U.S. Patent Application PublicationNo. 2015/0013981) which is incorporated by reference in its entirety.

In accordance with the present invention, there are several factorsrelevant to determining the appropriate construction of a heat pipe,including mechanical, thermal and environmental requirements.

A thermal evaluation of the potential effectiveness of the heat pipeincludes examining the heat pipe power capacity limits of the fluid, orthermosiphon, used in the heat pipe. There are limiting factors forthermosiphons, including entrainment of flooding limits and boiling orevaporative limits. For example, water has a greater power capacity thanmethanol or other fluids when in the 100° C. to 200° C. range. The powerlimit of the thermosiphon depends on the gravity return of thecondensate form of the fluid. The capillary limit does not apply and theviscosity limit is not an issue at higher temperatures. The sonic limitexceeds 2 kW at 100° C. and scales with the cross-sectional area of theheat pipe. The surface smoothness of the heat pipe also effects boilingof the thermosiphon. It is expected that entrainment is the mainlimiting factor where shear stress from the vapor flows up the heatpipe, which can prevent the counter flow of the condensate to theevaporator. This leads to “flooding” of the condenser.

A model can be used to estimate or project the entrainment or floodinglimit of the thermosiphon. Suitable models found in the art include, forexample: ESDU-81038 (1981) as reported in “Heat Pipes” by Dunn and Reay;Wallis (1969): Gas-liquid velocity criteria for flooding incounter-flow; Nguyen-Chi, H. and Groll, M.: Flooding Limit based onWallis criteria with additional term for tube inclination;Taitel-Duckler (1976): Criteria for Kelvin-Helmholtz instability forfinite waves in liquid films on inclined surfaces; and Weber numbercriteria with length scale based on the liquid film thickness. Anexample of an entrainment model estimating the liquid film thickness (t)in a tube 130 is shown in FIG. 13. In the example shown, the tube 130has width (w).

The liquid velocity profile is integrated to get mass flow according tothe following equation:

$Q = {\frac{\rho_{f}^{2}h_{fg}{wg}\; \cos \; \theta}{\mu_{f}}\left\lbrack {\frac{{t_{1}\left( {t_{1} + t_{2}} \right)}^{2}}{2} - \frac{\left( {t_{1} + t_{2}} \right)^{3}}{6}} \right\rbrack}$

The shear stress balance can be determined according to the followingequation:

$t_{2} = \frac{\tau_{v}}{\rho_{f}g\; \cos \; \theta}$

The unity Weber number can be determined according to the followingequation:

$Q \cong {\left( \frac{2{\pi\sigma\rho}_{g}h_{fg}^{2}}{Z} \right)^{0.5}{w\left( {w - t} \right)}}$

Table 2 shows predicted entrainment limited power:

TABLE 2 T_(vapor) = 121° C., Inclination = 60 degrees from vertical TubeID (in.) 0.237 1.1 3.31 Tube ID (mm) 6.02 27.9 84.1 Annulus ID (mm) 0 028 Number in Bundle 72 6 1 Entrainment Limited Power for IndividualPipes (kW) ESDU *0.5 0.35 15.5 102 Chi-Groll *2.2 0.40 18.2 141 Wallis0.43 20.3 156 Taitel Duckler *1.4 0.41 21.0 192 Entrainment LimitedPower for Assembly (kW) ESDU *0.5 25 93 102 Chi-Groll *2.2 29 109 141Wallis 31 122 156 Taitel Duckler *1.4 29 126 192 minimum 25 93 102maximum 31 126 192

With respect to the possibility of power capacity being limited byboiling, it is estimated that there would be heat flux levels of 3.4,7.5 and 22 W/cm² for tubes having inner diameters of 6, 28 and 84millimeters, respectively. At 100 kW total power over a 15 meter lengthfor the evaporator, the heat flux levels are 0.49, 1.26 and 2.53 W/cm²for tubes having inner diameters of 6, 28 and 84 millimeters,respectively. As a result, it is not expected that boiling of thethermosiphon should be a limiting condition for the heat pipes accordingto the invention.

It is estimated that for a heat pipe having a sixty degree inclinationfrom vertical and at 121° C., the power transport for a heat pipeincluding pipes having a ⅜ inch outer diameter and a seventy-two pipebundle (FIG. 14c ) would be 30 kW. It is further estimated the powertransport for a heat pipe under similar conditions having a 1.75 inchouter diameter and a six pipe bundle (FIG. 14b ) would be 100 kW. And itis further estimated that for a heat pipe under similar conditionshaving a 5.25 inch outer diameter and a single pipe (FIG. 14a ) would be120 kW.

A vapor shear test can be conducted with the purpose of determining theentrainment or flooding limited power capacity of a thermosiphon and toprovide a baseline for scaling to other tube sizes. The return of liquidcondensate by gravity down a thermosiphon tube is opposed by the shearstress from the counter-flow in vapor. The same shear stress conditionscan be created in an air-water analog in an open tube. Tests can be doneat different tube inclinations and liquid and gas flow rates todetermine the conditions where liquid is unable to flow down the tube.An apparatus for the test can include a glass tube having a length ofeight feet and an inner diameter of eight millimeters, pure deionizedwater introduced at the top of the tube, which flows down by gravity,and clean nitrogen gas introduced at the bottom of the tube, which flowsto the top and exits. Water wets the glass tube just as it wets thethermosiphon wall material and the normal liquid flow and flow reversalat higher gas velocities can be observed. The tests can be performed atroom temperature and the tube can be inclined at 30, 45 and 60 degreesfrom horizontal.

An energy equation is used to calculate mass flow rate of vapor andliquid and velocity of vapor. The shear stress is calculated based onvapor velocity for the round tube using standard friction factorcorrelations. The equivalent velocity of N₂ gas is calculated to matchvapor shear stress. Table 3 below shows test conditions to simulatewater liquid vapor counter-flow at 100° C. The flow becomes unsteady atthe conditions labeled with an asterisk in Table 3.

TABLE 3 Angle Fluid N₂ Gas Power Level of incline Flow rate Flow rateT_(a) [watts] From horizontal [mL/min] [gm/min] [° C.] 400 30° 10.64513.872 25 500 30° 13.306 17.340 25 600 30° 15.968 20.808 25 650 30°17.298 22.542 24.4 660 30° 17.564 22.889 24.4  670*  30°* 17.831* 23.235* 24.4*  680*  30°* 18.097*  23.582* 24.4*  690*  30°* 18.363* 23.929* 24.4*  700*  30°* 18.629*  24.276 * 24.4* 650 45° 17.298 22.54224.4 660 45° 17.564 22.889 24.4 670 45° 17.831 23.235 24.4 680 45°18.097 23.582 24.4 690 45° 18.363 23.929 24.4 700 45° 18.629 24.276 24.8710 45° 19.002 24.623 24.8 720 45° 19.27 24.969 24.8 730 45° 19.5425.316 24.8  740*  45°* 19.8*  25.663* 24.8*  750*  45°* 19.96* 26.01*24.8* 710 60° 18.895 24.623 23.6 720 60° 19.161 24.969 23.6 730 60°19.427 25.316 23.6 740 60° 19.694 25.663 23.6  750*  60°* 19.96* 26.01*23.6*  760*  60°* 20.226*  26.357* 23.6*  770*  60°* 20.492*  26.703*23.6*  780*  60°* 20.758* 27.05* 23.6*

A shear test shows that as the angle of inclination of the pipe or tubeincreases, the power carrying capacity also increases to a limit. Fromtesting an eight feet section of eight millimeter (inner diameter)tubing, it is estimated a pipe can carry from 600 W at an angle ofinclination from horizontal of 30 degrees up to 750 watts at an angle ofinclination of 60 degrees. Increasing the angle from 30 to 45 improvesthe power capacity by approximately 10%, but increasing the 45 to 60improves the power carrying capacity by only 1.3%. Further, a secondtube shaped with helical swirls around a W″ mandrel was built and testedwhich produced similar results, indicating the heat pipe will functionwith a transposed tube winding.

As shown and described in reference to FIGS. 7a-7c , there are severaldesign options for heat pipes and heat pipe bundles. Further examples ofheat pipe bundle design options are shown in FIGS. 14a -14 c.

FIG. 14a shows a heat pipe 150 having a single pipe 152 with a centralchamber 151 defining an inner diameter. FIG. 14b shows a heat pipebundle 160. The bundle 160 is formed by six heat pipes 162 around acentral chamber 161, with each of the six heat pipes 162 having a tubeor chamber 163 defining an inner diameter of the heat pipe 162. FIG. 14cshows a further heat pipe bundle 170. The heat pipe bundle 170 includessix smaller heat pipe bundles 174 around a central chamber 171. Eachsmaller heat pipe bundle 174 includes twelve heat pipes 172, each havinga tube or chamber 173 defining an inner diameter of the heat pipe 172.There are a total of seventy-two heat pipes 172 in the bundle 170.

FIGS. 15a-15c show the heat pipes 150, 160, 170 of FIGS. 14a-14c inthree-dimensional representations.

As the number of heat pipes increases from a heat pipe 150 to the heatpipe bundle 170, the diameter of the individual heat pipes 150, 162, 172decreases. Exemplary dimensions for the heat pipes 150, 160, 170 ofFIGS. 14a-14c that would fit a bore hole are listed in Table 4.

TABLE 4 Single Tube Six tubes 72 tubes (FIG. 14a) (FIG. 14b) (FIG. 14c)# of tubes 1    6    72-90 Outer Diameter (OD) 5.25″ 1.75″ 0.375″ Innerdiameter (ID) 3.31″ 1.10″ 0.237″ Wall Thickness (WT)  0.970″ 0.32″0.069″ OD/WT Ratio 5.4  5.4  5.4   Center hole diameter 1.5″  1.75″1.75″  Length 100′    100′    100′   

The material used for making the heat pipe wall may also vary based oncompatibility with water as the working fluid, corrosion resistance tobrine in the well bore, availability of tubes in the appropriatediameter and wall thickness material cost and ability to manufacture.One possible material is copper, which has a high thermal conductivity,compatibility with water as the working fluid, has well-knownfabrication processes and is readily available at the lowest cost. Asecond material option is 70/30 cupro-nickel alloy, which is consideredbecause of its excellent corrosion resistance and higher mechanicalstrength over copper. It is expected that it is compatible for makingheat pipes having water, as a related material, Monel, is known to beacceptable. A third material for possible use is titanium KS50, whichhas superior mechanical strength, half of the weight of copper andexcellent corrosion resistance. It is also known to be compatible withwater for heat pipe use.

These three pipe materials are further compared in Table 5 below:

TABLE 5 Cu—Ni Titanium Copper 70/30 Grade 2 CP (CDA 102, (CDA (ASTMCommercial Availability Units 122, 110) 715) B-338) Density lb./in³ .321.322 .163 Yield Strength kpsi 10 35 40 Ultimate strength kpsi 35 65 50Young's Modulus ×10⁶ psi 15.1 18 15.2 Weight to Stiffness ratio 47 47 93(2x) Percent Elongation % 40% 29% 10% to failure Coefficient of Thermal10⁻⁶ in/ 9.4 8.6 5.2 Expansion (@350° F.) in - ° F. Thermal ConductivityW/m-K 390 29.4 18.5 (RT) Corrosion Resistance Good Better Best

A stress analysis, as a result of bending of the material, can beperformed for each of these materials. Because the metals beingconsidered are ductile, the analysis compares the calculated stressvalues to the yield stress. Yield stress is usually measured as 0.2%yield or proof strength, which is the stress that produces a 0.2% strainwithout recovering. Stresses investigated in the analysis includebending around a large radius during installation and hoop stressescaused from internal tube pressures at 350° F. and 600° F. temperaturesand external pressures at 6,000, 8,000 and 10,000 feet below groundlevel. The bending stresses are calculated using Hooke's Law, where thestrain at the extreme fiber of the tube outer diameter, and E is themodulus of elasticity in 10⁶ pounds per square inch (psi). Strain rateis determined from bending around the large radius, the appendage thatmust pass through during deployment into the hole. Strains can bedetermined for a forty feet and fifty feet bend radius. Hoop stressescan be determined using Lame's equation.

A summary of the bending stress analysis is shown in Table 6. Theresults labeled (*) indicate a possibility of the tube to yield duringdeployment, the results labeled (**) indicate an elastic tube, and theresults with no asterisks indicate the tube will yield duringdeployment.

TABLE 6 Bending Stress, kpsi 5.25″ 1.75″ ⅜″ Bend Temp, OD OD OD Radius °F. Material tube tube tube 40 350 Cu, annealed 82.5 27.5 5.9 ** 40 600Cu, annealed 77.7 25.9 5.6 ** 50 350 Cu, annealed 66 22   4.7 ** 50 600Cu, annealed 62.2 20.7 4.4 ** 40 350 70/30 Cu—Ni, annealed 98.3 32.8 7.0** 40 600 70/30 Cu—Ni, annealed 92.8 30.9 6.6 ** 50 350 70/30 Cu—Ni,annealed 78.7   26.2 * 5.6 ** 50 600 70/30 Cu—Ni, annealed 74.2  24.7*5.3**  40 350 KS-50 Titanium 83.3  27.8** 5.9**  40 600 KS-50 Titanium75.3  25.1** 5.4**  50 350 KS-50 Titanium 66.6  22.2** 4.8**  50 600KS-50 Titanium 60.3  20.1** 4.3** 

A sample analysis of the estimated cost for the three example rawmaterials is shown in Table 7:

TABLE 7 Units Cu Cu—Ni Ti Raw material cost $USD/lb. $4 $22 Tube Cost$/lb. 5.33 9.14 $30-60 (?) Weight of Heat Pipe Assembly per foot Singletube Lbs./ft. 50.28 50.44 25.42 Six Tubes Lbs./ft. 33.52 33.63 16.95 72Tubes Lbs./ft. 18.47 18.53 9.34 Estimated Cost Per Heat Pipe Single tube$/ft. $268 $461 $782 Six Tubes $/ft. $178 $307 $522 72 Tubes $/ft. $98$169 $287

A summary of the estimated raw material cost tradeoffs for the threeexample materials is shown in Table 8:

TABLE 8 Units Single Tube 6 Tube 72 Tube Power Carrying Capacity kW 120100 30 Cost Per Watt Cu $/watt $.22 $.18 $.32 Cu—Ni $/watt $.38 $.31$.56 Ti $/watt $.65 $.52 $.96

While there have been shown and described and pointed out fundamentalnovel features of the invention as applied to preferred embodimentsthereof, it will be understood that various omissions and substitutionsand changes in the form and details of the devices and methods describedmay be made by those skilled in the art without departing from thespirit of the invention. For example, it is expressly intended that allcombinations of those elements and/or method steps which performsubstantially the same function in substantially the same way to achievethe same results are within the scope of the invention. Moreover, itshould be recognized that structures and/or elements and/or method stepsshown and/or described in connection with any disclosed form orembodiment of the invention may be incorporated in any other disclosedor described or suggested form or embodiment as a general matter ofdesign choice.

What is claimed:
 1. An apparatus for transporting geothermal heat from ageothermal well to a surface comprising: at least one heat pipecomprising a wall surrounding a central tube or chamber; a fluidcontained within the central tube or chamber; a first apparatus end thatis closed and positioned at a first end of the heat pipe, and a secondapparatus end that is closed and positioned at a second end of the heatpipe; wherein the apparatus is configured to be in a vertical orinclined position in the geothermal well, and wherein the fluid absorbsgeothermal heat at the first apparatus end as it transitions to a vapor,rises to the second apparatus end, releases geothermal heat at thesecond apparatus end as it condenses back to a liquid state, and returnsto the first apparatus end.
 2. The apparatus of claim 1, wherein thefirst apparatus end is configured for placement in the geothermal welland the second apparatus end is configured for placement near thesurface.
 3. The apparatus of claim 1, wherein the wall of the at leastone heat pipe further comprises: a copper layer surrounding the centraltube or chamber; a steel layer surrounding the copper layer; and atitanium layer surrounding the steel layer; and wherein at least thecopper layer and the titanium layer are non-porous to water.
 4. Theapparatus of claim 1, wherein the wall of the at least one heat pipefurther comprises: an internal coating layer surrounding the centraltube or chamber; an iron layer surrounding the internal coating layer,which is configured to protect the iron layer from the fluid in thecentral tube or chamber; and an external coating layer of a causticresistant material surrounding the iron layer; and wherein at least theinternal and external coating layers are non-porous to water.
 5. Theapparatus of claim 1, wherein the at least one heat pipe is made fromtitanium.
 6. The apparatus of claim 1, wherein the at least one heatpipe comprises: a plurality of pipes welded together vertically; a basesection secured to a base of the plurality of pipes; a threaded plugconfigured to be secured to an uppermost pipe of the plurality of pipes,which comprises corresponding threading; and a port comprised in theuppermost pipe of the plurality of pipes and positioned so as to becovered by the threaded plug when the threaded plug is fully insertedinto the uppermost pipe; and wherein during assembly of the at least oneheat pipe, the threaded plug is partially inserted into the plurality ofpipes, the fluid is injected into the at least one heat pipe through theport, and the threaded plug is then inserted further into the pluralityof pipes to cover the port.
 7. The apparatus of claim 6, wherein theplurality of pipes, the threaded plug and the base section are made fromtitanium.
 8. The apparatus of claim 1, wherein the at least one heatpipe comprises a plurality of heat pipes arranged in a bundlesurrounding a bundle central tube or chamber comprising the fluid. 9.The apparatus of claim 8, wherein the bundle of heat pipes comprises atleast six heat pipes surrounding the bundle central tube or chamber,each of the heat pipes comprising the wall surrounding the central tubeor chamber.
 10. The apparatus of claim 8, wherein the bundle of heatpipes comprises a plurality of bundles of heat pipes.
 11. The apparatusof claim 10, wherein the plurality of bundles of heat pipes comprises atleast six bundles of heat pipes and comprises a total of at leastseventy-two heat pipes.
 12. The apparatus of claim 11, wherein theplurality of bundles of heat pipes are arranged to surround a furthercentral tube or chamber comprising the fluid.
 13. The apparatus of claim1, wherein the at least one heat pipe comprises appendages branchingoutwardly from a central heat pipe configured to insertion intohorizontal or angled bore holes in the geothermal well.
 14. Theapparatus of claim 1, wherein the at least one heat pipe is made fromcopper.
 15. The apparatus of claim 1, wherein the at least one heat pipeis made from a copper-nickel alloy.
 16. The apparatus of claim 1,wherein the fluid is water.